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    A Polarised Population of Dynamic MicrotubulesMediates Homeostatic Length Control in Animal Cells

    Remigio Picone1,2,3,4, Xiaoyun Ren5, Kenzo D. Ivanovitch4, Jon D. W. Clarke5, Rachel A. McKendry2,3*,

    Buzz Baum4*

    1 Centre for Mathematics and Physics in the Life Sciences and Experimental Biology, University College London, London, United Kingdom, 2 London Centre for

    Nanotechnology, London, United Kingdom, 3 Department of Medicine, University College London, London, United Kingdom, 4 Medical Research Council Laboratory forMolecular Cell Biology, University College London, London, United Kingdom, 5 Medical Research Council Centre for Developmental Neurobiology, Kings College London,

    London, United Kingdom

    Abstract

    Because physical form and function are intimately linked, mechanisms that maintain cell shape and size within strict limitsare likely to be important for a wide variety of biological processes. However, while intrinsic controls have been found tocontribute to the relatively well-defined shape of bacteria and yeast cells, the extent to which individual cells from amulticellular animal control their plastic form remains unclear. Here, using micropatterned lines to limit cell extension to onedimension, we show that cells spread to a characteristic steady-state length that is independent of cell size, pattern width,and cortical actin. Instead, homeostatic length control on lines depends on a population of dynamic microtubules that leadduring cell extension, and that are aligned along the long cell axis as the result of interactions of microtubule plus ends withthe lateral cell cortex. Similarly, during the development of the zebrafish neural tube, elongated neuroepithelial cellsmaintain a relatively well-defined length that is independent of cell size but dependent upon oriented microtubules. A

    simple, quantitative model of cellular extension driven by microtubules recapitulates cell elongation on lines, the steady-state distribution of microtubules, and cell length homeostasis, and predicts the effects of microtubule inhibitors on celllength. Together this experimental and theoretical analysis suggests that microtubule dynamics impose unexpected limitson cell geometry that enable cells to regulate their length. Since cells are the building blocks and architects of tissuemorphogenesis, such intrinsically defined limits may be important for development and homeostasis in multicellularorganisms.

    Citation: Picone R, Ren X, Ivanovitch KD, Clarke JDW, McKendry RA, et al. (2010) A Polarised Population of Dynamic Microtubules Mediates Homeostatic LengthControl in Animal Cells. PLoS Biol 8(11): e1000542. doi:10.1371/journal.pbio.1000542

    Academic Editor: Alex Mogilner, University of California, Davis, United States of America

    Received March 11, 2010; Accepted October 1, 2010; Published November 16, 2010

    Copyright: 2010 Picone et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

    Funding: RP was funded by EPSRC Studentship (A.J.S.) awarded as part of the CoMPLEX Doctoral Training Centre (UCL) and IRC in Nanotechnology (Cambridge,

    UCL, Bristol). BB was funded by Cancer Research UK, Wellcome, UCL and the Royal Society. RAM was funded by UCL and the Royal Society and XR and JC werefunded by the BBSRC. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

    Competing Interests: The authors have declared that no competing interests exist.

    Abbreviations: 19s, 19 somite; ConA, Concanavalin A; DAPI, 49-6-diamidino-2-phenylindole; DCX, doublecortin; DMEM, Dulbeccos Modified Eagle Medium;dsRNA, double-stranded RNA; PDMS, polydimethylsiloxane; RNAi, RNA interference.

    * E-mail: [email protected] (RAM); [email protected] (BB)

    Introduction

    The physical properties of a system depend to a large extent

    upon its scale. Therefore, it is not surprising to find that many

    biological structures are maintained within relatively tightly

    constrained size limits [1,2]. In some cases, the dimensions of

    macromolecular assemblies are enforced by molecular rulers

    like titin, which helps to govern the length of the sarcomericrepeats in muscle [3]. However, many seemingly stable structures,

    such as metaphase spindles [4] and cilia [1], exist in a state of

    dynamic equilibrium in which a stable form arises from the

    collective action of a large number of molecular machines

    functioning in concert. Although mechanisms have been proposed

    for the control of the length of such polymers [1], through for

    example length-dependent microtubule depolymerisation [5], little

    is known about this fundamental and widespread biological

    phenomenon.

    For unicellular organisms, intrinsic mechanisms have been

    identified that regulate cell shape [2,6], maintain a steady-state cell

    size, and couple cell length and size [7]. However, it remains

    unclear whether similar controls regulate the dimensions of cells

    from multicellular animals, which, by virtue of not having a cell

    wall, assume a form that is plastic and a variable size, both of

    which depend to a large degree upon the extracellular tissue

    environment in which cells find themselves [8,9]. Nevertheless,

    since form and function are intimately linked and vary from cell

    type to cell type, it seems likely that the shape of many animal cellswill be maintained within intrinsically defined limits. Such

    behaviour has been observed in assays of cell spreading [10] and

    cell migration on planar adhesive substrates [11,12]. Moreover,

    studies of cells on grooved, scratched, or patterned substrates have

    in some cases [13,14] revealed limits to cell extension. In addition,

    regulated changes in cell geometry have long been known to drive

    a variety of morphogenesis movements in developing animals.

    During Drosophiladevelopment, for example, changes in epithelial

    cell shape and height are thought to drive internalisation of the

    ventral furrow [15]. Similarly, during neural tube development in

    zebrafish, individual neuroepithelial cells act together to form a

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    double-layered epithelium with a defined width, even under

    conditions in which the entire structure is mis-positioned or

    duplicated [16].

    Here, to systematically investigate the mechanisms that control

    animal cell geometry, we employed micro-contact printing [17] to

    generate adhesive lines of extracellular matrix that limit cell width

    but leave cells free to regulate their geometry in the other two

    dimensions (length and height). This analysis of cells spreading on

    adhesive lines reveals that animal cells can spread to a

    characteristic steady-state length that is independent of cell size,

    pattern width, and cortical actin, but is dependent on a population

    of microtubules that aligns along the long axis of cells as the result

    of interactions between microtubule plus ends and the cell cortex.

    Similarly, a population of oriented microtubules mediates length

    control in epithelial cells of the developing zebrafish neural tube. A

    mathematical model shows that cell length homeostasis in these

    cases can be quantitatively explained by the collective action of

    dynamic, orientated microtubules as they drive cell extension and

    undergo cortex-dependent catastrophe. Together, this experimen-

    tal and theoretical analysis reveals a role for microtubules in

    homeostatic cell length control in HeLa cells, DrosophilaS2R+ cells,

    and zebrafish neuroepithelial cells, suggesting that it may be an

    important general feature of animal cell biology.

    Results

    Cells on Micropatterned Lines Spread to a Steady StateLength That Is Independent of Pattern Width and CellSize

    To explore the intrinsic regulation of cell shape, we began by

    seeding a population of freshly harvested exponentially growing

    HeLa cells onto micropatterned fibronectin lines (Figure 1A)

    ranging in width from 3 to 35 mm, separated by non-adhesive

    polyethylene glycol, and onto equivalent non-patterned areas of

    the substrate (Figure 1B). Other researchers previously performed

    similar experiments by plating cells on grooved or scratched

    substrates [1820] or on adhesive strips [13]. In our case, after

    allowing 2 h for cells to adhere to and spread on the

    micropatterned substrate, cell length was monitored using semi-

    automated software designed to remove user bias and to facilitate

    the analysis of large datasets (Figure S1). Cell length for this

    analysis was defined as the maximum distance, parallel to the

    patterned line, separating extensions at distal cell tips (Figure 1A).

    Unexpectedly, cells from an exponentially growing population(with a wide range of masses) spread to a relatively well-defined

    average length of 44610 mm, which proved largely independent of

    line width and similar to that of cells on non-patterned substrates

    () (Figure 1C). Cell spreading in this assay was accompanied by a

    corresponding change in cell height, as expected if cell volume isconserved (Figure 1E and data not shown). These observations

    were similar to those previously reported for fibroblasts on

    scratched substrates [13]. Because a fixed-time-point assay was

    used for this analysis, however, the independence of cell length and

    pattern width could be the result of either a constant rate of cell

    spreading or the action of a cell length control mechanism. When

    live-cell imaging was used to examine the kinetics of cell spreading,

    we observed HeLa cells spreading monotonically over a period of

    approximately 60 min, reaching a steady-state length that was

    independent of pattern width (Figure 1D and 1E). These datasuggest that HeLa cells have an intrinsically defined length.

    To determine whether cell length control is a peculiarity of

    HeLa cells spreading on a fibronectin substrate or a more general

    feature of animal cell biology, we repeated these experiments using

    the adherent Drosophila hemocyte-derived S2R+ cells [21], which

    are significantly smaller than HeLa cells (with a mean volume,

    measured using an automated cell counter, of 1,177664 mm3 for

    Drosophila S2R+ cells compared to 2,12161,116 mm3 for HeLa

    cells; Figure 2A). These cells do not adhere well to fibronection-

    coated substrates, but could be induced to spread on glass dishes

    coated with Concanavalin A (ConA) [15]. Once spreading was

    complete (5 h after plating), the length of these cells was measured.

    Like HeLa cells, patterned S2R+ cells were found to achieve a

    reproducible steady-state length that was relatively independent of

    their width (Figure 2B and data not shown). Moreover, despite

    their very different average volumes, S2R+ and HeLa cells had

    comparable resting lengths (5569 mm and 44610 mm, respec-

    tively). This observation suggested the possibility that the limit of

    an animal cells long axis might be regulated independently of its

    volume. As a direct test of this hypothesis we altered the culturing

    conditions to obtain a population of HeLa cells grown to

    confluence that had an average volume of 1,2336835 mm3 (about

    half that of HeLa cells grown to 50% confluence; Figure 2A).

    When the two populations of differently sized HeLa cells were

    plated onto micro-contact-printed fibronectin lines of varying

    widths for 2 h, they were found to spread to statistically similar

    lengths (Figure 2B) despite having different heights (data not

    shown), confirming the independence of cell length and volume.

    Cell Length Control Is Dependent on a Population ofOriented Microtubules

    It seemed unlikely that cell length control depends on plasma

    membrane tension, since dramatic changes in cell volume and linewidth had little impact on the length of HeLa or S2R+ cells, or on

    the spreading kinetics of HeLa cells on narrow and thick patterned

    lines (Figure 1D). In searching for mechanisms underlying cell

    length control we therefore turned to examine a possible role for

    the cytoskeleton [22], since actin filaments and microtubules have

    been implicated in the control of fixed-length structures [1,3,23]

    and in the regulation of cell length [6,13] and cell spreading

    Author Summary

    Because many physical processes change with scale, sizecontrol is a fundamental problem for living systems. Whilein some instances the size of a structure is directlydetermined by the dimensions of its individual constitu-ents, many biological structures are dynamic, self-organis-ing assemblies of relatively small component parts. Howsuch assemblies are maintained within defined size limits

    remains poorly understood. Here, by confining cells tospread on lines, we show that animal cells reach a definedlength that is independent of their volume and width. Insearching for a ruler that might determine this axial limitto cell spreading, we identified a population of dynamicmicrotubule polymers that become oriented along thelong axis of cells. This growing population of orientedmicrotubules drives extension of the spreading cell marginwhile, conversely, interactions with the cell marginpromote microtubule depolymerisation, leading to cellshortening. Using a mathematical model we show that thiscoupling of dynamic microtubule polymerisation anddepolymerisation with directed cell elongation is sufficientto explain the limit to cell spreading and cell lengthhomeostasis. Because microtubules appear to regulate cell

    length in a similar way in the developing zebrafish neuraltube, we suggest that this microtubule-dependent mech-anism is likely to be of widespread importance for theregulation of cell and tissue geometry.

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    Figure 1. Length homeostasis in HeLa cells on patterned fibronectin lines. (A) HeLa cells on patterned 13-mm-wide fibronectin-FITC lines(green) were fixed and stained with TRITC-phalloidin to label actin filaments (red) and DAPI to label DNA (blue). Images depict xzand xyprojections.The length of HeLa cells on patterned lines was defined as the distance, parallel to the patterned line, between distal-most cell extensions. (B) Thelength of cells on non-patterned fibronectin surfaces was defined as the greatest distance between any two points along the cell boundary (Feretsdiameter). (C) Lengths of Hela cells were measured yielding an average length of 44610 mm (n= 759) on patterned lines and 4464 mm (n= 603) onnon-patterned surfaces (). Dotted line indicates the lengths predicted for a constant cell height. (D and E) Hela cells spreading on lines of widths 310 mm and 2535 mm were tracked and cell length semi-automatically calculated. During the first 60 min, the spreading velocity was 0.660.5 mm/min (n= 18) and 0.560.5 mm/min (n= 13) for narrow and wide patterned lines, respectively. Cells reached a steady-state length after ,60 min.Orange line (D) and rectangle (E) indicate standard 120-min observation point as used in (C). Scale bars= 10 mm. Error bars denote upper and lowerbox plot quartiles.doi:10.1371/journal.pbio.1000542.g001

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    [18,2427]. We began by analysing the cytoskeletal changes that

    accompany cell spreading on micropatterned lines. Following

    attachment to a patterned surface and a brief period of blebbing

    (Figure 1E), cells developed spreading lamellipodia that quickly

    reached the edges of the patterned lines. While lamellipodia

    reaching laterally outside of the pattern into regions passified with

    polyethylene glycol underwent periodic cycles of extension and

    retraction [28], lamellipodia extending in the direction of cell

    elongation remained tightly bound to the adhesive substrate (data

    not shown). To test whether these actin-based lamellipodia play arole in cell elongation or cell length control, we took advantage of

    the efficacy of RNA interference (RNAi)mediated gene silencing

    in fly cell culture to target SCAR/WAVE (hereafter SCAR) to

    selectively remove these structures from spreading cells [29]. Five

    days after treatment with control (LacZ) or SCAR double-stranded

    RNA (dsRNA) [30,31], Drosophila S2R+ cells were seeded onto

    non-patterned substrates (Figure 3A and 3B) and onto micro-

    patterned ConA lines (Figure 3C). Cell length was then assayed

    5 h later (Figure 3D). As Figure 3C shows, SCAR RNAi cells

    assumed their typical RNAi phenotype, in which lamellipodia are

    replaced by long, radial, microtubule-rich processes [31]. Despite

    this, the majority of microtubule-based protrusions became

    oriented along the ConA lines. When we measured the distance

    parallel to the pattern between distal protrusion tips in these cells,

    we found that the length of SCAR RNAi cells was statistically

    indistinguishable from that of control cells (Figure 3D). Similarly,

    control RNAi and SCAR RNAi cells reached similar steady-state

    spread diameters on non-patterned substrates [31] (Figure 3D).

    Thus, although SCAR is required for the formation of

    lamellipodial-based protrusions, lamellipodial actin is not requiredfor cell elongation and does not alter the steady-state length of

    microtubule-rich extensions. We then repeated these experiments

    in HeLa cells, using a Rac inhibitor [32] to compromise

    lamellipodial formation (Figure 3F). As with S2R+ cells, this did

    not alter cell length (compare Figure 3F and 3G). To test a possible

    role for actin-myosin-mediated cortical tension in the regulation of

    cell length, we also carried out a similar analysis using blebbistatin

    to inhibit Myosin II [33]. Once again, this did not affect the rate of

    cell spreading (Figure 3H and 3I) or resting cell length (54.3 [28,

    +17] mm for HeLa cells [n = 345] on fibronectin lines, and 50.9

    [24, +11] mm for HeLa cells [ n = 52] on non-patterned

    fibronectin) (Figure 3E). Although surprising, these data concur

    with previously reported work showing that the final spread area of

    fibroblasts and HeLa cells is relatively independent of membrane

    tension [34] and cortical actin [10].Having failed to identify a role for the actin cytoskeleton, these

    data prompted us to examine the function of microtubules, which

    have previously been implicated in cell spreading [20,2426,35]

    and in the generation of an elongated cell shape [36,37].

    Strikingly, in the presence of the microtubule inhibitor colcemid

    [38], HeLa cells were unable to elongate (Figure 4A and 4D). This

    effect was reversible since cells re-spread to their characteristic

    length after the drug was washed out and the microtubule

    cytoskeleton re-established (Figure 4C, 4E, and 4F). Cell spreading

    in this system therefore requires microtubules. To gain mechanis-

    tic insight into their precise role, we then analysed microtubule

    organisation at intervals during cell spreading (Figure 5). Cell

    elongation was accompanied by a progressive polarisation of the

    microtubule cytoskeleton, as microtubules concentrated on thebasal part of the cell (Figure S3) became aligned along the long cell

    axis (Figure 5B and 5D; quantified in Figure 5F). Strikingly, a

    similar re-alignment was observed over shorter time scales as

    individual growing microtubules in cells at steady state became

    oriented to lie along the long cell axis (Figure 6A), as the result of

    contacts between growing microtubule plus tips (marked with

    EB3-GFP) and the ruffling cell margin at the interface between an

    adhesive and non-adhesive substrate (Figure 6B and 6C). This

    cortex-induced change in microtubule direction was similar to that

    previously described in yeast [6], animal cells [20,39], and plant

    cells [40].

    Interestingly, the fate of each growing microtubule meeting the

    cortex depended strongly on the angle of contact (Figure 6B, 6C,

    and 6E), such that microtubule plus ends contacting the cortex at a

    steep angle (32u90u from the long line axis) underwentcatastrophe, while others contacting the cortex at less of an angle

    (0u25u ) changed their direction of growth to run parallel to the

    cell edge. This explains the low probability of finding microtubules

    aligned at an angle of between 30u and 90u with respect to the long

    cell axis in Figure 5 (or 230u and 290u according to the notation

    in Figure 6C). As a result of this angular dependency, the

    microtubule cytoskeleton reached a highly polarised equilibrium

    state, with the majority of microtubules running along the cell edge

    (Figure 6A; quantified in Figure 6F; explained in Figure 6G).

    Importantly, this angular dependency of microtubule catastrophe/

    bending resulted in overt polarisation of the microtubule

    Figure 2. Cell length is not dependent on cell width, volume, orsubstrate type. (A) The volumes of S2R+ cells (green) and HeLa cellsgrown to 50% (orange, used in Figure 1) and 100% confluence (blue)were measured using a Coulter Counter. (B) Cells from these three cellpopulations were plated onto adhesive lines (ConA for S2R+ cells andfibronectin for HeLa cells) 335 mm in width and onto equivalent non-patterned surfaces (), and cell lengths were quantified. Error barsdenote upper and lower box plot quartiles.doi:10.1371/journal.pbio.1000542.g002

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    Figure 3. The extension limit ofDrosophilacells is independent of lamellipodial actin. (AC) S2R+ cells treated for 5 d with LacZ (control)or SCAR dsRNA were plated onto ConA lines and non-patterned ConA substrates (A). Depletion of SCAR produces spiky cells that lack all lamellipodia.Images show (A) a LacZ RNAi cell fixed and stained for actin filaments (red) and microtubules (green), and an equivalent SCAR RNAi cell on a non-patterned substrate (B) and a patterned ConA line (C). (D) The average lengths of SCAR RNAi S2R + cells on patterned lines and on a non-patternedsurface () were calculated as 55613 mm (n=43) and 5268 mm (n= 23), respectively. The equivalent measurement for LacZ RNAi cells was58615 mm (n= 66). (EG) Lengths of HeLa cells treated with blebbistatin (40 mM) (E), NSC23766 (Rac inhibitor) (40 mM) (F), or DMSO (G) on fibronectinpatterned lines and a non-patterned surface. (H and I) Plots show changes in the length of HeLa cells (determined after fixation) during a time course

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    cytoskeleton. We also observed oriented microtubules leading

    during cell extension (Figure 6D and 6F; Video S1, S2, S3). Taken

    together these data suggest that microtubules oriented parallel to

    the adhesive boundary are strong candidates for drivers of cell

    spreading and the source of intrinsic cell length control.

    A Simple Model of Microtubule-Based Cell SpreadingRecapitulates Cell Length Control

    To test whether the dynamic behaviour of this oriented array of

    microtubules could define cell length in this system, we generated

    a simple mathematical model of microtubule-based cell length

    control (Figures 7 and 8). In contrast with previous models of cell

    spreading [10,41,42], our model was constructed to assess the

    effects of a polarised array of dynamic microtubules on cell

    elongation and homeostasis. Based upon our analysis of the

    cellular distribution of microtubules (Figures 5 and 6), EB3-GFP

    comets (Figure 6D), and c-tubulin (Figure S2), microtubules in themodel were assumed to grow out from the cell centre towards cell

    tips (Figure 7A). Cycles of dynamic instability were then

    implemented using values of growth and catastrophe rates takenfrom the experimental literature [43]. The interaction between

    microtubules and the cell cortex was then modelled by assuming

    that contact (i) increases the microtubule catastrophe rate (by a

    factor of 16 [43]) and (ii) drives the extension of the cell margin

    [44]. (Although the mechanism by which this occurs is not

    specified in the model, we think it likely that it is through the

    delivery of new material required for local growth [24] rather than

    through force generation [45,46].) A slow fixed rate of margin

    retraction was then implemented, based upon measurements of

    the rate of retraction of cells on lines in the absence of

    microtubules (0.460.3 mm/min), which may reflect the turnover

    of material from the cell periphery. Simulations using this simple

    scheme were found to recapitulate the path of cell elongation and

    cell length homeostasis (Figure 7A7C). Furthermore, the modelpredicts a linear decrease in microtubule density from the cell

    centre to the cell edge, which was verified experimentally

    (Figure 7D). Interestingly, the model also revealed that, irrespec-tive of the actual cell length, it is the small number of dynamic

    microtubules (approximately two) that reach the cell cortex thatmaintain cell length homeostasis, by countering the tendency of

    the cell margin to retract (Figures 7C and S4). This is in line with

    previous data suggesting that a small population of pioneer

    microtubules is sufficient in some systems to drive forward

    movement of the cell edge [47].

    When we examined the effects of varying the remaining freeparameters in the model (Figure 8A8C), we found that cell length

    homeostasis (the coefficient of variation in cell length) was

    marginally sensitive to changes in the value of a, representing

    the level of microtubule cooperation in the system (Figure 8A8C),and to changes in Nm, the number of cooperating microtubules.

    Based on measurements of cell length and microtubule numbers in

    HeLa cells on lines, we were able to estimate the value ofa as 8,implying that individual microtubules cooperate to drive cell

    spreading. More significantly, an analysis of the effects of varying

    the other experimentally determined parameters in the model

    revealed that cell length control critically requires a high value of

    cB/cI, the ratio of the microtubule catastrophe rate at the cortex

    (cB ) to that in the cell interior (cI ). Thus, cell length becomes

    progressively more variable as the ratio ofcB/cI is reduced, e.g., as

    cB tends to 0 (Figures 8D, 8E, and S4B). By contrast, changes in

    the microtubule polymerisation rate (vg ) induce corresponding

    changes in cell length in the model without inducing a loss of

    homeostasis (Figures S4A, 9A, and 9B), causing the system to

    stabilise at a new steady-state length when the number of

    microtubule plus ends interacting with the cell cortex returnedto the equilibrium value of,2 (Figure 9B). This serves as a good

    test of the likely effects of the addition of a microtubule inhibitor

    on cell length control (Figure 9A and 9B). To test whether this

    prediction is borne out in experiment, we used an inhibitor of

    microtubule dynamics [38] to reduce the rate of microtubule

    polymerisation in HeLa cells on lines of varying width at steady

    state. After allowing cells 2 h to spread, 40 nM colcemid or an

    equivalent amount of the carrier DMSO was added to the

    medium for 30 min (Figure 9C9E). In the case of colcemid, but

    not DMSO, this was sufficient to disturb microtubule organisation

    without causing a complete loss of microtubules (data not shown),

    and induced active cell shortening (Figure 9C and 9D). As

    predicted, cells settled down to a new shorter length following this

    treatment, irrespective of line width (Figure 9C and 9D). We

    conclude that the dynamic behaviour of the population of

    longitudinally polarised microtubules plays a key role in

    homeostatic cell length control.

    An Oriented Population of Microtubules ControlsEpithelial Height in the Developing Zebrafish NeuralTube

    Previous work has suggested roles for microtubules in the

    regulation of cell shape in 3-D environments [48]. Therefore, we

    were prompted to test whether cells exhibit a similar type of cell

    length homeostasis in a tissue and developmental context. We used

    the zebrafish neural tube as a simple model system for this analysis

    for several reasons. First, cells in this tissue are bipolar in form and

    of similar length to S2R+ and HeLa cells on lines. Second, once

    formed [16], this tissue is maintained as a stable structure

    consisting of two parallel columns of highly elongated neuroep-

    ithelial cells [49], making reliable measurements of cell length

    relatively easy. Third, the tissue is amenable to imaging and

    perturbation experiments using morpholinos. To begin, we tested

    whether cell length depends upon cell volume in the zebrafish

    neural tube by arresting cells in the G2 phase of the cell cycle using

    an established protocol in which a morpholino against the

    translational start site of the G2/M regulator Emi1 (Emi1-MO)

    or a control morpholino (Con-MO) is injected into the one-cell

    embryo [50,51]. As previously reported, this treatment does not

    affect cell division until the neural plate stage because of a

    maternal effect and has very limited cytotoxicity [50,51]. For

    consistency across animals, measurements of cell lengths were then

    made using the neuroepithelium of the hindbrain close to thedeveloping otic vesicle in 19 somite (19s)stage embryos. At this

    stage in development the neural tube has not yet inflated its

    ventricle, and neuroepithelial cells from the left and right sides

    meet in the middle of the tube, as confirmed by the expression of

    the polarity protein Par3-GFP, which reveals the apical ends of all

    cells lining up along the tube midline in both control and emi1

    morphant embryos (Figure 10A). This block in cell cycle

    progression (evident in the loss of pH3 staining in Figure 10A)

    led to a significant 2.6-fold increase in neuroepithelial cell volume

    (Figure 10B; Emi1-MO, 9,034.263,839.3 mm3, n = 7 cells from

    three embryos; Con-MO, 3,516.46608.2 mm3, n = 8 cells from

    following treatment with blebbistatin (40 mM) (red circles) or DMSO (black diamonds) on thin ([H], 3 to 15 mm) or thick ([I], 16 to 35 mm) patternedfibronectin lines. Scale bar= 10 mm. Error bars denote upper and lower box plot quartiles.doi:10.1371/journal.pbio.1000542.g003

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    Figure 4. Microtubules lead elongation of HeLa cells on patterned line. Colcemid (1 mM) depolymerises microtubules ([A], compare with [B])and stops cell elongation on fibronectin patterned lines (2362 mm, n= 12) (D). After drug wash out microtubules re-grow and cells elongate (C),reaching a characteristic length of 42611 mm (n= 38) (E). (F) shows average lengths of cells in DMSO solution at 15 min (2062 mm, n=15) and 2 h(43610 mm, n= 35). In (DF) average length is measured for DMSO- or colcemid-treated cells fixed at various times (15 min, 1 h, 2 h, and 3 h) afterattachment to patterned lines. Scale bar = 10 mm. Error bars denote upper and lower box plot quartiles.doi:10.1371/journal.pbio.1000542.g004

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    four embryos; t test, p = 0.007) when compared to control-

    morpholino-injected embryos. The variability in the extent of

    volume increase observed likely reflects the slight variability of the

    timing with which the Emi1-MO-induced cell cycle arrest kicks in

    in different embryos.

    Since the vast majority of individual cells in the tissue span the

    entire width of the neural tube (Figure 10A), we were able to use

    the width of the tissue at three locations close to the otic vesicle to

    estimate average cell length. Despite the large difference in cell

    volumes between control and emi1 morphant embryos (readily

    visible in embryos labelled with Par3-GFP and H2B-RFP;

    Figure 10A), the length of neuroepithelial cells remained unaltered

    (Figure 10C; Con-MO, 44.9763.66 mm, n = 10; Emi1-MO,

    48.1166.83, n =10; t test, p = 0.188). This shows that cell length

    is independent of cell volume in this tissue context as it is in our

    cell culture models.

    To test whether microtubule dynamics are required to define

    cell length in this system, we visualised microtubule cytoskeletal

    organisation within the neuroepithelium. Stochastic labelling of

    cells in the neural tube with GFP fused to the microtubule-

    Figure 5. Microtubules become polarised during cell elongation and control cell length homeostasis. HeLa cells spreading on a non-patterned (A) or patterned (B) fibronectin substrate were fixed and microtubules labelled (green) 0, 30, and 90 min after attachment. Binary images ofmicrotubules (C and D) were automatically processed (E and F) to reveal the extent of microtubule polarisation. This is depicted as an angularprobability distribution for straight microtubules in non-patterned cells (n= 4) and in patterned cells at 0 min (n= 1), 30 min (n= 5), and 90 min (n= 4)after attachment. Microtubule polymer orientation was determined by normalising the amount of linear tubulin polymer at each angle by the totalamount of linear polymer in the cell. Microtubules were identified based on overlap with straight lines (red line in [C]).doi:10.1371/journal.pbio.1000542.g005

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    associated protein doublecortin (DCX) [52] revealed bundles of

    parallel microtubules running the entire length of each neuroep-

    ithelial cell (Figure 10D), from the apical to the basal limit of the

    epithelium. To determine whether these microtubules function in

    cell length control, as was shown for microtubules in cells on

    micropatterned lines, we added low doses of the microtubule

    inhibitor nocodazole to these embryos for a period of 30 min.

    While high doses of microtubule inhibitors lead to a reversible loss

    Figure 6. The fate of growing microtubules, to bend or to undergo catastrophe, depends on the contact angle with which theymeet the cell cortex. (AD) EB3-GFP-labelled microtubule plus ends were tracked in the perinuclear region of an HeLa cell, close to the site atwhich the majority of microtubules are nucleated ([A], nucleus labelled by white dotted line). Growing EB3-GFP-labelled microtubules that interactwith the cell cortex (dotted circles) either bend to change direction ([B], red arrowhead, EB3-GFP spot 1) or undergo catastrophe ([C], yellowarrowhead, EB3-GFP spot 2). Through this process, a majority of microtubule plus ends become oriented parallel to the cell long axis and movetowards the cell ends ([D], white arrowhead, EB3-GFP spot 3). (E) The fate of microtubules contacting the cell cortex depends on the contact angle(n= 39). An angle of between225u and 25u (red) leads to a change in direction, whereas an angle of between 32u and 90u (or between 290u and232u, yellow), leads to catastrophe. For microtubules with contact angles between 25u and 32u (or 232u and 225u), bending or catastrophe eventsappear to occur with similar probability. The black arrowheads in (E) refer to the EB3-GFP-labelled microtubules marked in (BD). Quantitativelysimilar results were seen for EB1-GFP-labelled microtubule plus ends in S2 cells (see Video S3). (F) Microtubule (MT) density is shown plotted againstcell width for HeLa cells on pattern lines at steady state (like that shown on right). Microtubule intensities were measured in cells (n= 20) labelled with

    FITC-conjugated anti-a-tubulin antibodies within regions just distal to the nucleus (examples marked by the rectangles in the right-hand image).Average microtubule numbers were then determined by normalising the intensity signal based upon the fluorescence of single microtubules. Thehistogram insert shows average number of microtubules (1165) aligned within ,30% of the cell edge along the lateral edge of cells (marked in redin large graph). These regions lead during cell elongation (see cell on right). (G) Diagram showing polarisation of microtubules (green lines) and thecell cortex (red rectangle) as the result of interactions between microtubules and the lateral cell cortex. Depending on the angle of incidence, contactinduces microtubules to re-orient along the long cell axis (blue arrow heads) or to undergo catastrophe (orange Ts). Scale bar = 5 mm. Error barsdenote the standard deviation.doi:10.1371/journal.pbio.1000542.g006

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    of neuroepithelial form as all the cells in the tissue round up (data

    not shown), this treatment leaves overall tissue architecture intact

    (Figure 10E). The result was a significant reduction in the width of

    nocodazole-treated neural tubes when compared to those in

    DMSO control embryos (Figure 10F), without affecting differences

    in width that characterise different parts of the tissue. Moreover, as

    the concentration of nocodazole was increased, the neural tube

    became progressively narrower (DMSO, 49.3763.11 mm, n = 8;

    5 mg/ml nocodazole, 48.9962.73 mm, n = 9; 10 mg/ml nocodazole,

    46.9363.29 mm, n =8; 20 mg/ml nocodazole, 43.7761.99 mm,

    n = 7). This analysis suggests that the parallel bundles of microtu-

    bules seen spanning the entire width of the epithelium within

    individual neuroepithelial cells play a critical role in the ability of

    cells to maintain their length and proper tissue architecture, as they

    do in homeostatic length control in cells in culture.

    Discussion

    Taken together our analysis of hemocyte-derived Drosophila cells

    and epithelial-derived HeLa cells on micro-contact-printed lines in

    culture, and of neuroepithelial cells in the developing zebrafish

    neural tube, identifies a capacity for animal cells to maintain an

    intrinsically defined length. Cell length control in these systems

    appears to act independently of cell width and volume. Instead, it

    relies on the continuing presence of a polarised population of

    dynamic microtubules that, as a result of interactions with the cell

    cortex, come to lie parallel to the long axis of cells, running from the

    centre to either cell tip. Because cell extension depends on

    microtubules, this oriented array of dynamic microtubules is thenin a position to regulate cell length. Somewhat surprisingly, we

    observed no role for actin-based cortical tension in opposing

    microtubule-driven cell elongation in our system. This is in line with

    data from previous studies showing that the final cell spread area is

    independent of the actin cytoskeleton [10,24]. Because of this, cell

    length control is unlikely to reflect a balance of forces between

    contractile actin filaments and extending microtubule rodsas

    previously hypothesized for the regulation of animal cell form [22].

    In fact, a recent study showed that microtubules do not bear a

    significant mechanical load in fully spread cells [53]. Based on these

    observations, it seems likely that microtubules drive cell elongation

    through the promotion of directional traffic of material from the

    Golgi to the cell surface [24], rather than through the direct

    generation of mechanical force itself. Interestingly, microtubule

    dynamics have also been shown to contribute to (i) the regulation ofcell length and cell shape in fission yeast via the regulation of cell

    transport [54], (ii) axial elongation in plant cells [55], and (iii) the

    maintenance of spindle length within defined limits [56]. As such,

    limits to the length of dynamic microtubule-based structures may be

    a relatively widespread phenomenon in biology.

    Recently, a mechanism for length-dependent microtubule

    depolymerisation was discovered [5], which could help to explain

    the regulation of processes such as cell length. While this

    mechanism may be involved in cell length control, our analysis

    suggests that it may not be necessary to invoke this type of control

    to understand the maintenance of microtubule-dependent struc-

    Figure 7. A model constructed based upon the interactionbetween parallel microtubules and a free cell edge. See Materials

    and Methods for more details. (A) Simulation of cell extension forNm = 11 and a= 8 (other model parameters as shown in Table 1). Themodel was then used to explore the role of microtubule (green lines)number (Nm) and the extent of microtubule cooperation (a) in cellelongation (red line) and cell length control. (B) Cell elongation kineticsobserved in the model using a= 8 and Nm = 11 (other modelparameters as in Table 1) recapitulates that seen in experiments.Stochastic simulations of cell elongation kinetics are shown in gray andaverage values in green. (C) Numbers of microtubule (MT) plus endscontacting the cell end during cell elongation in simulations using a= 8and Nm = 11 (other model parameters as in Table 1). (D) Changes inmicrotubule density were plotted along the long cell axis for cells in themodel (blue line) and in experiment (red line) at steady state. Changesin experimentally determined microtubule fluorescence and microtu-

    bule density obtained from simulations are shown as percentages ofcell length, so that values across cells could be grouped to assessaverage cell behaviour. (Inset) To calculate the microtubule densityacross the edge of a HeLa cell on a patterned line, we measuredmicrotubule (green) fluorescence intensity over the half cell length(scanning line in red) within 30% of the cell margin (i.e., within theyellow lines). Scale bar = 10 mm. Error bars denote the standarddeviation.doi:10.1371/journal.pbio.1000542.g007

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    tures within relatively well-defined size limits in all cases, since cell

    length control can arise as a relatively simple by-product of

    microtubule-based cell extension if a few simple propositions hold.

    These propositions are the following: (i) that dynamic microtubules

    are polarised so that they polymerise along the long cell axis

    towards cell tips, (ii) that the rate of microtubule catastrophe

    increases when microtubules reach the cells ends, and (iii)

    that microtubules act together to prevent retraction of the cell

    margin and promote cell elongation, probably through the

    delivery of material to counter turnover of material at the cell

    tips. Significantly, a model based on these experimentally well-

    established assumptions predicts the spreading dynamics weobserve on patterned lines, the steady-state microtubule distribu-

    tion (Figure 7D), the path of cell elongation (Figures 9A, 9B, and

    S4B), and the effects of a microtubule poison on cell length

    (Figure 9C and 9D).

    Intrinsic regulation of cell length in a tissue and developmental

    context is inherently difficult to demonstrate unambiguously

    because of the potentially confounding effects of forces and signals

    from neighbouring tissues and extracellular matrix. For example,

    tissue architecture and the dimensions of neuroepithelial cells in

    the newly formed zebrafish neural tube are likely to be influenced

    by both extrinsic and cell-intrinsic factors, as cells undergo

    interdigitation and intercalation across the midline [16,57].

    Moreover, zebrafish neuroepithelial cells achieve their final length

    through a complex mechanism involving initial overextension and

    then retraction (data not shown) as they establish a nascent apical

    domain at the tissue midline [16]. Because tissue architecture in

    this case is generated via a complex process of self organisation, an

    intrinsic mechanism that biases cell length may be indispensable to

    ensure robust organ size and form in the face of variations in the

    volume of component cells and variations in the movements and

    differentiation of surrounding tissues [58]. Indeed, here we show

    that neuroepithelial cell length in vivo is independent of cell

    volume but, consistent with our findings in vitro, dependent on apopulation of axially oriented microtubules. As a result, increasing

    levels of microtubule inhibitors administered over a relatively short

    period of time cause systematic reductions in epithelial height

    (Figure 10C). These data help to explain how it is that

    neuroepithelial height can remain relatively unchanged in ectopic

    neural tubes that are not situated at the embryonic midline in

    morphogenetic mutants (compare cells in Figure 4C and 4F in

    [16]; compare cells in Figure 1G, 1H, and, 1K in [57]).

    Similar conclusions can be drawn from earlier studies on the

    effects of cell cycle arrest on development [59,60], where it was

    noted that many ultrastructural features and functional properties of

    Figure 8. The role of parameters in the model on cell length homeostasis. (A) Cell length distributions were calculated from simulationsusing parameter values shown in Table 1 and a= 8 for different numbers of microtubules (Nm = 216). (B) Cell length distributions were calculatedfrom simulations using parameter values shown in Table 1 and Nm = 11 for different levels of microtubule cooperation (a= 016). (C) To more fullyexplore the effects of different values ofNm and a (other model parameters as in Table 1) on cell length homeostasis, variation in cell length (standarddeviation values are shown in colour using the colour-map shown) was measured over 10,000 min of simulation time. Homeostasis is achieved for abroad range of parameters above a low threshold value ofa. (D) Cell length distributions with same mean values were calculated in the model fordifferent values ofcB/cI from model simulations with a= 8 and Nm = 11, using vg and vB values shown in Table 1. (E) In a cell at steady state, a dramaticreduction in the value of the cell boundary catastrophe rate, cB, produces a dramatic increase in the steady-state number of microtubules (MT) at cellboundary (in orange) and a steady increase in cell length over time (black dotted line). a= 8 and Nm = 12; model parameters cI, vg, and vB as shown in

    Table 1.doi:10.1371/journal.pbio.1000542.g008

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    cells were conserved despite dramatic changes induced in cell size.

    Our study shows that the regulation of neuroepithelial height is one

    way by which embryos are able to do this. More generally, one

    could hypothesize that cell length homeostasis is likely to be required

    in all growing epithelia that need to maintain apicalbasal structure

    despite continual changes in the volumes of their constituent cells.

    While the emphasis of this study is cell length homeostasis, it isclear that changes in animal cell length or height are likely to play

    a critical role during tissue morphogenesis in vivo. During

    Drosophila gastrulation, for example, epithelial cells are thought

    to actively contribute to ventral furrow formation by undergoing

    apical constriction and cell shortening [15], a process that would

    seem to require orchestrated changes in cell length. Although the

    mechanism by which this occurs is not understood, it is plausible

    that microtubules, which are highly polarised along the apical

    basal cell axis of Drosophila epithelial cells, play a role, as has been

    shown in other epithelia [61,62]. Similarly, the changes in cell

    length that accompany neuron and myoblast differentiation are

    brought about by changes in microtubule dynamics [6365].

    Thus, many animal cells are likely to need to be able to regulate

    their optimal steady-state length, e.g., by changing the rate of

    microtubule polymerisation to alter their resting length whilst

    preserving length control (Figures 9A and S4A). Conversely,

    decreasing the susceptibility of microtubules to undergo catastro-

    phe at the cell cortex, e.g., by crosslinking microtubules withMap1A [63], could induce dramatic but relatively unregulated cell

    elongation (Figure 8E). Because of this, long cells like neurons may

    rely on additional control systems, like length-dependent regula-

    tors of microtubule catastrophe [5] or environmental cues, to

    reach specific locations during the process of axon pathfinding. An

    important goal of future research will be to identify how intrinsic

    length constraints and additional layers of control are altered

    during animal development to give specific cells and tissues their

    characteristic forms, and to determine whether the deregulation of

    cell length control contributes to the loss of tissue homeostasis seen

    in diseases such as cancer.

    Figure 9. Testing the model of microtubule-based cell length homeostasis. (A and B) Model cell length dynamics (A) and numbers ofmicrotubules (MT) interacting with the cell margin (B) were analysed as the microtubule polymerisation rate, vg, was changed by a factor of 0.75(orange) or 0.5 (red). (Nm = 11 and a= 8; other parameters were fixed.) (CE) As a test of this model, 40 nM colcemid (D) or an equivalent volume ofDMSO (E) was added to HeLa cells on lines of varying widths (310 mm, 1115 mm, 1620 mm, 2125 mm, and 2635 mm) at steady state, and averagecell length was measured. An HeLa cell spreading on a fibronectin line is shown (C) before and after treatment with 40 nM colcemid (at 120 min,indicated by orange arrow). The green dotted line indicates expected length without perturbation. Orange dotted line indicates measured celllength. Scale bar = 10 mm. Error bars denote upper and lower box plot quartiles.doi:10.1371/journal.pbio.1000542.g009

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    Materials and Methods

    Cell Culture MethodsMicro-contact printing and cell patterning. Micro-contact

    printing was carried out as described previously [66]. A master (or

    template) was used to generate a polydimethylsiloxane (PDMS)

    stamp. Briefly, the master was fabricated as follows. In a clean room,

    a 4-in. silicon wafer was cleaned under nitrogen and spin-coated at

    3,000 rpm for 2030 s with 2 ml of S1818 (Shipley) positive resist toobtain a wafer with a ,2-mm-thick resist coating. The wafer was

    then baked on a hot plate at 100uC for 1 min and the positive resist

    exposed to 6 mW/cm2 UV light at 405 nm (KARL SUSS aligner

    MJB 3UV 300) for 3050 s. The exposed areas of the S1818

    positive resist were then removed by dipping the wafer in a solution

    of microposit developer (35i, Shipley). The wafer was manually

    agitated for ,1 min and rinsed using de-ionised H2O. The

    developing procedure was repeated three times and the master

    dried under a stream of nitrogen gas, before being baked again for

    1 minon a hot plate at100uC. The PDMS stamps (Sylgard kit, Dow

    Corning) were made by using a previously described method [66].

    The PDMS stamps were cleaned by sonication in 70% EtOH for

    5 min, rinsed with de-ionised H2O, under a stream of nitrogen gas,

    and inked for 10 min in a solution of 10 mg/ml fibronectin (Sigma-

    Aldrich) together with 10 mg/ml fibronectin-FITC (Sigma-Aldrich)

    conjugated in PBS, or in a solution of 5 mg/ml ConA together with

    5 mg/ml ConA-FITC (Sigma-Aldrich) conjugated in distilled water

    (for S2R+ cell patterning). After inking, PDMS stamps were dried

    under nitrogen gas and placed in contact with a glass coverslip

    (VWR International) that had been plasma-cleaned and coatedwith non-adhesive polyethylene glycol, PLL-g-PEG (SUSOS,

    Switzerland), for 1 min.

    Before patterning, cells were washed in fresh serum-free

    medium (M3 at 24uC for Drosophila S2R+ cells and DIMEM at

    37uC for HeLa cells). Cells were trypsinized (using Trypsin-

    EDTA, Invitrogen) and their volume assessed in a Coulter

    Counter (Multisizer II, Beckman-Coulter) at a 1:10 dilution in

    Isoton II (Beckman-Coulter). The remainder were resuspended in

    serum-free medium at a density of 104 cells/cm2 and seeded on

    the micropatterned coverslips. Typically, cells attach to the printed

    ConA or fibronectin within 10 min of seeding. After 30 min, non-

    Figure 10. Zebrafish neural tube width is not affected by increases in cell volume but is sensitive to low levels of nocodazole. (A) Inthe left panels neural tubes (outlined with white dots) were visualised with membrane GFP (mGFP), imaged from dorsal view, and measured at threepositions (orange dotted lines) around the otic vesicle (asterisk), and the measurements were averaged. Lack of anti-phospho-histone H3 (anti-PhH3)staining in lower panel indicates that Emi1-MO effectively blocks cell divisions. (Midline of neural tube indicated by black arrowhead. Scalebar=50 mm.) In right panels embryos are expressing Par3-GFP to reveal the nascent apical surface of the neural tube and H2B-RFP to reveal theenlarged nuclei of the division blocked in emi1 morphant embryos (sections viewed in near transverse plane). (B) Cell volume is significantly larger inemi1 morphants (Emi1-MO) than it is in control embryos (Con-MO). (C) Neural tube width was not significantly different between Con-MO and Emi1-MO embryos. (D) Zebrafish embryos were injected with a plasmid expressing DCX-GFP to visualise the microtubule cytoskeleton and mRNA encoding

    Cherry-CAAX to visualise the neural tube cells. Microtubule bundles were present along the entire length of labelled cells. (Midline indicated by blackarrowhead. Scale bar= 10 mm.) (E) Neural tube structure is not affected by treatment with low levels of nocodazole. Zebrafish embryos were injectedwith mRNA encoding Cherry-CAAX and H2B-RFP and treated with nocodazole at different concentrations. Scale bar: 50 mm. (F) The neural tube ofnocodazole-treated embryos was narrower than that of control embryos, and epithelial width was reduced in a concentration-dependent manner.doi:10.1371/journal.pbio.1000542.g010

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    adherent cells and debris were removed by replacing the medium

    with fresh serum-free medium. Serum-free medium was used to

    avoid the effects of ECM proteins in serum.

    Cell culture. Drosophila S2R+ cells [67] were cultured in M3

    media (Sigma-Aldrich, S3652) with 10% heat-inactivated fetal

    bovine serum (12103-78P, JRH Biosciences) as monolayers at

    room temperature (2225uC) in treated culture flasks (Falcon, BD

    Biosciences). HeLa cells were cultured in Dulbeccos Modified

    Eagle Medium (DMEM) supplemented with 10% heat-inactivatedfetal bovine serum and 1% Pen-Strep (Sigma-Aldrich). Drosophila

    cells were propagated and treated with dsRNA as previously

    described [37,68]. For SCAR/WAVE dsRNA synthesis, primer

    sequences flanked with T7 sites were chosen for amplification of

    300600 bp of exonic sequence with smaller than 21-bp stretches

    of identity with any other gene. PCR products were then used as a

    template for the MEGAscript T7 reaction. RNAi was performed

    on S2R+ cells cultured in four-well tissue culture plate. Five days

    after RNAi, cells were gently removed from the plate, resuspended

    in Sang M3 Insect media (S3652, Sigma-Aldrich) and seeded on

    ConA patterns as described above. Small HeLa cells were

    obtained by using cells close to 100% confluency (measured by

    Coulter Counter, Multisizer II, Beckman-Coulter). For all other

    experiments, we used HeLa cells growing at 50% confluency (2 d

    after splitting a confluent culture 1:10).Drug treatment. In order to destabilise microtubules in cells

    in culture, 40 nM or 1 mM demecolcine (colcemid, Sigma-Aldrich,

    in DMSO) was added to HeLa cells on lines 90 min after seeding.

    A 40-nM dose was sufficient to alter microtubule organisation

    without altering microtubules organisation. A 1-mM dose was

    sufficient to depolymerise all microtubules. An equivalent amount

    of DMSO was used in control experiments. To alter cortical

    contactile forces, 40 mM blebbistatin, a non-muscle Myosin II

    inhibitor (B0560, Sigma-Aldrich) [33], was added to 50%

    confluent culture of HeLa cells. After 30 min of drug incubation

    the cells were gently trypsinized, and resuspended in DMEM with

    40 mM blebbistatin, after 20 min cells were plated onto the

    micropatterned lines. An equivalent amount of DMSO was used

    in control experiments. After prolonged periods of time, this led toa majority of multinucleate cells as expected as the result of defects

    in actin-myosin-based cytokinesis (data not shown). The

    destabilisation of the actin lamellipodium in HeLa cells was

    achieved using NSC23766 (Calbiochem) [32], a Rac inhibitor.

    NSC23766 (40 mM) was added to 50% confluent culture of HeLa

    cells. After 30 min of drug incubation the cells were gently

    trypsinized and resuspended in DMEM with 40 mM NSC23766

    and after 20 min plated onto the micropatterned lines. An

    equivalent amount of methanol was used in control experiments.

    Immunofluorenscence microscopy. HeLa cells stably ex-

    pressing live-act-GFP [69] were used for live-imaging experiments.

    For imaging actin filament organisation, S2R+ and HeLa cells

    were rinsed in PBS, fixed with 4% paraformaldehyde at room

    temperature, washed with PBS, permeabilized with 0.1% Triton

    X-100 in PBS, blocked for 1 h with 5% BSA in PBS, and stainedwith phalloidin-TRITC (1/400, Sigma-Aldrich), 49-6-diamidino-

    2-phenylindole (DAPI) (1/1,000, Sigma-Aldrich), and a FITC-

    conjugated GM1a anti-a-tubulin antibody (1/400, Sigma- Aldrich). After staining, coverslips were washed in PBS,

    mounted on microscope slide under 20 ml of reagent (FluorSave,

    Calbiochem), and dried at 40uC for 1 h. To better visualise the

    microtubule organisation, cells were fixed with 220uC 100%

    methanol for 4 min. After 4 min, cells were rinsed in PBS, and

    microtubules immune-labelled using the FITC-conjugated GM1aanti-a-tubulin antibody. To visualise microtubule plus ends, HeLaand S2 cells were transfected with EB3-GFP and EB1-GFP,

    respectively, and, analysed 48 h after transfection. Chemically

    fixed and live cells were imaged using a Leica SP5 inverted

    confocal microscope or a Nikon TE2000 inverted microscope.

    Image and data analysis. Images of cells on lines were

    acquired automatically using a 206/0.45 N.A. objective on a

    Nikon TE2000, and Metamorph software (Universal Imaging) to

    drive an automated Prior stage. Cell length and microtubule

    polarity data were measured using in-house automated software

    that was designed to remove user bias and to analyse largedatasets. For the measurement of cell length (Figure S1C), images

    of cells were thresholded for segmentation, mononucleate cells

    selected, and maximum cell length parallel to the line measured.

    Pattern width (Figure S1B) was calculated empirically from images

    of fluorescent lines in each case. To analyse microtubule

    organisation, grayscale images of cells were processed using a

    median filter and thresholding. The probably of finding

    microtubule polymer oriented in a given direction in Figure 5

    was determined by normalising the amount of linear tubulin

    polymer at that angle by the total amount of linear polymer in the

    cell. In-house software was developed in Java (http://www.java.

    com) and integrated in ImageJ (http://rsbweb.nih.gov/ij/). The

    data analysis was mainly performed using R environment (http://

    www.r-project.org/) and Matlab.

    Mathematical Model of Microtubule-Based Cell Extension A mathematical model was formulated to examine the likely

    role of microtubules in the control of cell length. The model was

    based on experimental observations that microtubules aligned

    along the long axis of the cell, with plus ends towards the cell tips

    (Videos S1, S2, S3), appear to drive the elongation of cell edges on

    adhesive lines (Figure 4A4F) and in cells lacking lamellipodia

    (Figure 3). Using this as a framework, we constructed a simple

    stochastic half-cell model of cell elongation driven by a population

    of parallel dynamic microtubules. Where possible, parameters

    used to model microtubule dynamics were taken directly from

    experimental data (see Table 1). We then made a number of

    simplifying assumptions. First, we assumed that a fixed number of

    microtubules, Nm, nucleate at the cell centre and grow towards thecell ends at a rate determined by the known rate of microtubule

    polymerisation, vg, with an experimentally defined cytoplasmic

    catastrophe rate cI [43], and we made the simplifying assumption

    that there is no rescue of microtubule growth following

    catastrophe. Upon reaching the cortex (defined as the region

    Table 1. Model parameters.

    Parame-

    ter Type Parameter Symbol Value Unit

    Fixed Microtubule growth velocitya vg 1564 mm min21

    Microtubule catastrophe

    internal ratea

    cI 0.3 min21

    Microtubule catastropherate at cell boundarya

    cB 4.8 min21

    Cell boundary retraction rateb vB 0.460.3 mm min21

    Free Total number of nucleationsites

    Nm .0

    Cooperative behaviour ofindividual microtubules tocell elongation constant

    a .0

    aValues from [43].bValues from experimental data in this study.doi:10.1371/journal.pbio.1000542.t001

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    within 3 mm of the cell boundary), microtubule plus ends then act

    together to promote extension of the cell boundary. We modelled

    the cooperative effects of n microtubules touching the cortex in

    driving cell elongation at each time step using the function e2a/n.

    Because microtubules can drive cell elongation through forces

    generated by the addition of tubulin subunits [70], through the

    delivery of new material required for local growth, and/or through

    local modification of the cell cortex [45,46], in this study a is

    assumed to be a free, dimensionless parameter. At the same time,in line with cell biological data, contact with the cortex induces an

    increase in the rate of microtubule catastrophe cB [43] (See

    Table 1). Since catastrophe events free up a microtubule

    nucleation site in the model, the number of growing microtubules

    remains constant over time. Finally, the term vB was added, based

    upon experimental data (data not shown), to represent the slow

    retraction of the cell margin in the absence of microtubules

    (0.460.3 mm/min). After applying known rates of microtubule

    growth and catastrophe to the model (see Table 1), two free

    variables remain: a, which governs the cooperative effect of

    microtubules on the movement of the cell boundary, and Nm, the

    number of microtubule nucleation sites. In order to compare the

    results of simulations with experimental data from Figures 13,

    simulations were run in Matlab by using parameter values shown

    in Table 1, and the position of the boundary was used as a read

    out of half cell length.

    Based on this scheme, given a random number r in the interval

    [0,1], the stochastic equations that describe the microtubule

    growth in time are given by

    Lm(tzDt)~Lm(t)zDt vm(t) rDt cm(t)

    0 rvDt cm(t)

    1

    Lm(0)~0

    Where Lm is the microtubule length, r is a random number in the

    interval 0#r#1, Dt (0.001 min) is the simulation time step, and vmand cm are the microtubule velocity and catastrophe rates,

    respectively. The stochastic catastrophe event is defined by the

    random number r and Dt cm. In order to model cell extension, a

    cell length boundary equation LB is added to the model:

    LB(tzDt)~LB(t)zDt vg e

    {a=DmB(t)D DmB(t)Dw0

    LB(t){Dt vB DmB(t)D~0

    (2

    LB(0)~0

    where vg is the microtubule growing rate internal to the cell and vBis the cell boundary velocity retraction rate when there are no

    microtubules crossing the boundary. a governs the cooperativeeffect of microtubules in promoting cell boundary extension, as

    defined by the function e2a/|mB(t)|. mI and mB describe internal and

    boundary microtubules as follows:

    mB(t)~fm=Lm(t)LB(t) m [ 1,Nm\Qg 3

    mI(t)~fm=Lm(t)vLB(t) m [ 1,Nm\Qg 4

    Finally the general microtubule velocity and catastrophe rate

    equations are given by

    cm(t)~cB Vm [mB(t)

    cI Vm [mI(t)

    5

    vm(t)~vg e

    {a=DmB(t)D Vm [mB(t)

    vg Vm [mI(t)

    (6

    where cI and cB are the internal and boundary catastrophemicrotubules rates, respectively.

    The aim of our model was to quantitatively explore the

    relationship between microtubule behaviour and cell length

    control. Significantly, for a wide range of Nm and a values, this

    simple scheme recapitulated the path of cell elongation and length

    control seen in observations of cells on lines (Figure 1). As seen in

    experiments (Figure 1D), the rate of cell elongation in the model

    diminished over the course of 60 min, leading to a steady-state cell

    length within a few hours (Figure 7B). To understand the source of

    cell length homeostasis in these simulations we plotted the number

    of microtubules contacting the cell cortex over time (Figure 7C).

    This revealed a steady decrease in the number of microtubules

    reaching the cell cortex as cells elongate. As cells extend, this

    number plateaus, reaching a steady equilibrium between cell

    elongation and cell retraction that maintains cell length over time,

    which is typically approximately two microtubulesa number

    that is independent of the number of microtubule nucleation sites

    and cell length itself (Figure 7C). The model also predicted a linear

    decrease in microtubule density with distance from the cell centre

    similar to that measured in cells on lines (Figure 7D).

    Significantly, the number of microtubule nucleation sites, Nm,

    had little impact on the ability of cells to achieve length

    homeostasis (Figure 8A and 8B; cell length variance is used as

    quantitative measure of homeostasis), while a moderate level of

    microtubule cooperation (a.3) was required for a reproduciblecell length (Figure 8B and 8C). Above this threshold, while cells

    were able to maintain a homeostatic cell length irrespective of the

    specific values of Nm and a, cell length increased with increasing

    values ofNm and decreased with increasing values ofa (Figure 8C).Although catastrophe rates used in the model were based on

    experimentally well-defined parameters, we also determined the

    effects of changing the cortical cB and internal cI catastrophe rates

    on cell length homeostasis. This revealed that cell length control is

    gradually lost when cB/cI tends to zero, i.e., as cB values were

    reduced or cI increased. This is seen by the increase in cell length

    variancea quantitative measure of homeostasis (Figures 8D and

    S4B). It should also be noted that at values of cB close to zero, the

    number of microtubules at the cell boundary increases to a high

    steady-state value, driving continuous cell elongation (Figure 8E).

    Finally, the model was used to test the likely effects of colcemid in

    this system [38] by altering vg. A reduction in vg leads to a linear

    reduction in cell length (Figure S4A), as cells re-establish

    equilibrium with an average of approximately two microtubulescontacting the cell cortex per unit time (Figure 9A and 9B).

    Zebrafish MethodsCell cycle block and neural tube width

    measurements. To block cell division, zebrafish embryos

    were injected with 1 nl of 0.5 mM antisense morpholino against

    the start site of the early mitotic inhibitor 1 (Emi1-MO) [50,51].

    Standard control morpholino (Con-MO) (Genetools) was injected

    at the same concentration. To monitor the efficiency of the

    division block, embryos were immunostained with antibody

    against phospho-histone H3 (Upstate Biologicals).

    Homeostatic Cell Length Control

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    To visualise neural tube organisation, embryos were injected

    with either mRNA (100 pg) encoding membrane-GFP, or Par3-GFP and H2B-RFP. Capped mRNA was synthesised with

    mMessage Machine kit (Ambion).Neural tube cell volumes were calculated assuming the cell is a

    block, with height being the length of the long side of the cell,

    width being the length of the short side of the cell, and depth

    calculated from the number of confocal sections occupied by the

    cell. Measurements were taken from images of mosaically labelled19s embryos injected with mRNA encoding a membrane marker

    (mGFP or Cherry-CAAX) and H2B-RFP at 32- to 64-cell stage.

    To measure the width of the neural tube, embryos were fixed at

    19s, and confocal images of the hindbrain were taken from dorsal

    to ventral. To adjust for tilting of the neural tube, 3-D projection

    of the neural tube was generated using the 3D Projection Tool in

    ImageJ. Width of the neural tube was measured at three positions

    around the otic vesicle and averaged (Figure 10A).Microtubule visualisation and perturbation. To visualise

    microtubules, zebrafish embryos were injected with plasmid

    expressing DCX-GFP (generous gift from Steve Wilson,

    University College London). DCX-GFP was injected with

    mRNA encoding Cherry-CAAX and H2B-RFP to visualise cell

    outlines (data not shown). For drug treatment, nocodazole was

    dissolved in fish water from concentrated stock (5 mg/ml DMSO),and DMSO at 0.4% was used as vehicle control. The 19s embryos

    were then soaked in this medium for 30 min at 28uC before beingfixed. Neural tube width was measured as previously described.

    Supporting Information

    Figure S1 Image analysis of patterned cells. (A) Images ofTRITC-labelled F-actin in cells on lines were acquired in a vertical orientation. (B) The pattern width was calculated by

    averaging the widths obtained at the intersection of a scanninghorizontal line (blue line) with a binary pattern image (in black) as

    the scanning line moves vertically. (C) Lengths of patterned cells

    were obtained by fitting a rectangular shape to binary images of

    cells stained for F-actin and taking the length of the rectangle side

    parallel to the patterned line (yellow line). Lengths of non-patterned cells were obtained by taking the greatest distance

    possible between any two points along the cell boundary (Ferets

    diameter) (see Figure 1B). Only the length of mononuclear cells

    was measured. The cell ([A], yellow dotted) and the line pattern

    boundaries ([A], blue dotted) were obtained by thresholding image

    intensity. The cell and pattern boundary were successively filled

    inside and outside by black and white, respectively, to obtain the

    binary images shown in (B) and (C). Cell nucleus was segmented

    by the same method.

    Found at: doi:0.1371/journal.pbio.1000542.s001 (0.51 MB TIF)

    Figure S2 Microtubule nucleation. Microtubule nucleationsites in HeLa cells were labelled by c-tubulin first antibody (A) andAlexa Cy5 secondary antibody (B). Microtubules were labelled by

    FITC-conjugated anti-a-tubulin antibody (C). Nucleus waslabelled by DAPI (D).

    Found at: doi:0.1371/journal.pbio.1000542.s002 (2.53 MB TIF)

    Figure S3 Dynamic microtubules lie along the cell

    bottom, close to the substrate. (A) Dynamic microtubulesare concentrated within 1 mm of the substrate. Confocal zy-section

    projection of an HeLa cell transfected by EB3-GFP on a non-

    patterned fibronectin surface (B) and on a patterned fibronectin

    line (C). Top (D and E) and bottom (F and G) part of each HeLa

    cell transfected by EB3-GFP.

    Found at: doi:0.1371/journal.pbio.1000542.s003 (0.26 MB DOC)

    Figure S4 The effects of microtubule polymerisationrates on average cell length. (A) The microtubule growth rate(vg ) in the model was plotted against steady-state values of cell

    length. The model predicts a linear relationship between

    microtubule polymerisation rate and cell length at steady state

    (y = 1.7x22). (B) Variations in cell length (standard deviation) are

    shown for cells ,44 mm long following changes in the catastrophe

    rates of microtubules at the cell boundary, cB (in orange), or of

    cytoplasmic microtubules, cI (in green). Average values were

    obtained by examining the variance when length was chosen to be

    close to experimentally determined values, using values of Nm and

    a varying from 1 to 30 and from 0 to 30, respectively, while other

    parameters were kept constant (with values specified in Table 1).

    Found at: doi:0.1371/journal.pbio.1000542.s004 (2.58 MB TIF)

    Video S1 Microtubule plus ends in an HeLa cell on athin micropatterned line. EB3-GFP-labelled microtubule plus

    ends in an HeLa cell on a thin fibronectin patterned line (not

    shown).

    Found at: doi:0.1371/journal.pbio.1000542.s005 (1.33 MB MOV)

    Video S2 Microtubule plus ends in an HeLa cell on athick micropatterned line. EB3-GFP-labelled microtubule

    plus ends in an HeLa cell on a thick fibronectin patterned line (not

    shown).

    Found at: doi:0.1371/journal.pbio.1000542.s006 (0.97 MB MOV)

    Video S3 Microtubule plus ends in an S2 cell on amicropatterned line. EB1-GFP-labelled microtubule plus ends

    in an S2 cell on a ConA patterned line (not shown).

    Found at: doi:0.1371/journal.pbio.1000542.s007 (0.61 MB MOV)

    Acknowledgments

    We thank Tom Duke for reading of the manuscript; the Baum and

    McKendry lab for help throughout; Julia Palm for her help at early stages

    in the project; and Moyu Watari for critical discussion and insight. We also

    thank Steve Wilson for DCX-GFP and Masa Tada for the mRNA

    constructs.

    Author Contributions

    The author(s) have made the following declarations about their

    contributions: Conceived and designed the experiments: RP XR JDWC

    RAM BB. Performed the experiments: RP XR. Analyzed the data: RP

    XR. Wrote the paper: RP XR BB. Carried out all the zebrafish work: XR.

    Made the initial observations and developed the methods that led to thecurrent study: KDI. Co-conceived the zebrafish work: JDWC. Co-

    supervised the cell and micropatterning work: RAM.

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